Step 1. Throw this in front of your students:

Step 2. Give students some think time. Then collect responses however you want. Here are two options:

• If you have enough whiteboard space, give the entire class 60 seconds to write one of their equations on the board. Set a timer. Or count down during the final 10 seconds. Or both. Whatever the case, this needs to be quick. If time allows and you’re interested, select 2-3 equations for the class to verify.
• Are your students arranged in groups? Ask each group to contribute their favorite equation. Then give the class a couple minutes to hunt for “imposter” (i.e., incorrect) equations.

Samples. Here are some responses you might see for today (May 13):

Can I use your classroom as a remote laboratory? If you’re game, I’d love for you to run this by your students sometime this semester. If you do, drop a few words about your experience in the comments below.

Cheers!

Inspired by the sleepy looks on several faces, I interrupted my middle school class with a shout: “Everybody stand up! Head to the back of the room. Make a circle around those two tables.”

At this point, I had no idea what we were going to do. But it was going to be on our feet and it was going to involve everyone.

On the way to the back of the room, I snagged an empty water bottle. And then…

Round 1

Holding the plastic bottle in my hands, I announced: “2, 4, 6.” Then I passed the bottle to the student on my right, and gave her no directions.

Her response was beautiful: “2, 4, 6, 8?”

“Nice. But leave off the 2, 4, 6. Just say 8.” We started over. “2, 4, 6.” Then, “8.”

“Alright! Pass it along.”

The next student: “10.”

And with that, the rhythm was established. We went all the way around the circle. And guess what?! Eighth graders can count by twos!

Round 2

With the bottle back in my hands, I started a new routine: “5, 10, 15.” But then I passed it off to the left. And they rocked this direct variation sequence just as easily as the first round.

Round 3 (and a surprise!)

“Okay, let’s ramp up the difficulty just a bit. Ready? Here goes: 1, 4, 7.”

I passed the bottle along (back to the right now), and with no hesitation: “10.”

Then followed 13, 16, and 19 without any trouble. And to be honest, much of the progress was smooth, as you’d hope for a group of middle schoolers.

But once every third or fourth student, there was a pause. Not a long one. Not necessarily awkward. Just a pause. And that up-and-to-the-left-as-if-the-answer-is-on-the-ceiling look that means someone is lying (or telling the truth; I can never remember). There was a fair bit of whispering, followed by a shout: “20… 21… 22!” And even some twitching fingers as students accessed old-school strategies for continuing the pattern.

This was magic for me. I’ve only been teaching this group for about three weeks. (It’s a long story.) As such, I don’t know their strengths and weaknesses quite as well as if I’d been their teacher all year. But this simple activity gave me instant insight into the basic number sense skills my students possess.

There was another bonus at the end of this round. We briefly discussed the “starting number” and the “change” (1 and 3, respectively). Since we’ve been rocking linear visual patterns recently, we turned this into the equation y = 1 + 3x rather quickly and moved on. (Assuming that we’re beginning with the zeroth term here.)

Round 4 (another surprise!)

We had time for one more: “5, 9, 13.” I passed the bottle left, and we were off. “17,” “21,” and so forth. But then we hit a snag. Someone forgot the previous numbers. So we invented a new rule: If someone gets stuck, they can ask the previous three people to repeat their numbers. No other hints are allowed.

On track. Off track. Hint. Back on track. And so on until we make it back to the beginning.

Looking Ahead

I’m excited to try this again next week. I’ve already started thinking about ways to adjust and/or extend:

• Introduce a higher starting number, and/or negative change. (A student actually suggested 10, 8, 6, etc. as we wandered back to our seats.)
• Introduce sequences involving fractions or decimals.
• Invite students to generate the pattern by kicking a round off with their own sequence of three numbers.
• Mix things up—and simultaneously encourage more students to focus on each response—so that if a student needs help, I call on a random student to repeat the last 2-3 numbers.

One More Thing…

I can’t help but think I may be subconsciously ripping off Sadie Estrella’s counting circles here. Whatever the case, I’m excited to see where this routine leads us in the weeks ahead.

If you do something similar with your students, or if you decide to give this a try with your own class, drop a line in the comments so we can benefit from your experience.

And if your name is Sadie and you hail from the lovely state of Hawaii, there’s a special spot in the comments reserved just for you. Let me know what you think!

A while back I wrote about how this lovely game ventured from my childhood and into my classroom. My approach has shifted quite a bit (and for the better, I think) so I thought I’d share how we do things in class now.

Super Previously

When I first introduced this to my students, iOS didn’t exist. So each day we played, I simply pointed my web-browser (pre-Google Chrome, if you’ll believe it) to http://www.setgame.com and we played the free daily puzzle. Find the six sets in the set of 12 cards as fast as you can.

Students would raise their hands, I’d call on them as fast as my mouth could manage, they would shout three numbers quick as can be, and I’d click the corresponding cards on the screen. If all was well, we repeat that process five more times and cross our fingers in the hopes that we had the fastest time of the day/week/month/year/ever.

Previously

Several years later I got an iPad. And an Apple TV. And I forked over the 5 bucks for the iOS version of the Set Game. Instead of working through the free daily puzzle, I would offer my students a 60-second challenge. The beauty of this approach is that I could control the amount of time we spent playing Set on a given day (super previously, we would sometimes play for several minutes if the students had trouble finding the last couple of sets). Now it was 60 seconds, period. No more, no less. Aside from that, our style remained the same: Find a set, raise your hand, shout numbers. Repeat.

Now

One of the drawbacks of these original approaches is that they played to the strengths of the fastest students and ignored those who need more time to process. The start of class was a flurry of pattern-finding and number-shouting (quite impressive to watch as a visitor unfamiliar with the game), but it really depended on a select few; the majority of my students barely participated at all.

With that in mind, here’s how we play now:

1. I display a random, annotated image (hooray for screenshots on the iPad) from a ready-and-waiting Keynote file:

2. I give students “30 silent seconds to search” during which (as the description implies) they are to search, um, silently, for as many sets as they can find. (By the way, I’m taking attendance while they do this.)
3. Next, I announce that “you may now collaborate.” I wrap up attendance and get ready to call on groups.
4. I call on one group at a time, asking each group to announce the numbers of a single set.
5. I record the results on the board (regardless of any mistakes students might make), and proceed to the next group.
6. Once I get to the last group, I then open it up to “anyone in the class.”
7. Students continue sharing.
8. Once no more students are willing to share (and by this time we usually have 6-9 sets), I ask “Does anyone see any imposters?” (our name for mis-identified sets).
9. Imposters are identified, with brief explanations as to why the proposed trio of numbers is not actually a set. (Ex: “1, 2, 11, because two of them are singles.”)
10. Then we move on to whatever is next.

Advantages to this approach? I see a few:

• All students are given an opportunity to play
• Students are also given an opportunity to collaborate
• No one student or group is allowed to dominate when sharing proposed answers
• Students have a regular, bite-sized, built-in opportunity to “critique the reasoning of others” (SMP 3) when they identify imposters
• One last thing… Students love those black numbers on yellow squares, as it shifts the entire focus to visual pattern recognition (though I’m a bit sad that they benefit so greatly from this little trick, as I would prefer that they recognize the structure build into the 3×4 array)

In the Future

Recently, I’ve wondered about challenging students with the task of creating a set of 12 cards with exactly six sets. I anticipate this would be quite challenging, and there might be some interesting patterns and discussions that would arise along the way. I’ll keep you posted on this front. Or, if you beat me to the punch, let me know how you and your students fare.

Beyond Set

For me, this post is about much more than detailing the evolution of our Set Game exploits. The most important thread of this development is one that I hope will run through most of the lessons in my classroom. The challenge: While creating opportunities for engaging experiences, carve out space where every student has an opportunity to participate in a meaningful way. As I turn my attention from the Set Game to student activities, rich math tasks, and class discussions, I’ll pay closer to attention to whether my teaching decisions help or harm students in this regard. I challenge you to do the same.

I’ve been meaning to blog about the “assessment workflow” in my classroom, but I’ve been putting it off because (a) time is limited, especially at the end of the school year, and (b) I wanted to be mostly satisfied with my workflow before I shared anything (and I’m not there yet).

I’ll write up the full details of how assessment happens in my classroom (it’s been a major work-in-progress this year), but for now I want to share a tiny bit of background and then cut to today’s breakthrough.

The Background

Last Sunday I aired some of my thoughts and questions on this topic to @Mythagon. A few other thoughtful folks dropped by to share their own ideas and pose a few new questions for me to chew on. It left me with a clear sense (as have other conversations) that my assessment routine fails students in the category of self-feedback. I’ve been trying to foster more (and better) student reflection in our assessment routine for several months now, and those efforts are the reason I’ve pasted this quick reflection form…

…at the bottom of every new assessment I write. However, I was looking for a way to incorporate something that would require students to be more thoughtful (just shading in a couple of boxes doesn’t necessarily demand any careful consideration) and at the same time foster a growth mindset among my students.

The Breakthrough

At the end of today’s assessment (after grading them; more on that in the next post), just before collecting everything, I gave students the following directions:

Two minutes later, I collected the papers and we moved on to something else. Later in the day I went through the papers to confirm the results and scores, to get a sense of common mistakes (again, more on this workflow later), and (this part was new today!) to read the SP and STI comments.

Growth Mindset, Plans for the Future

It’s early, but I’m sensing that this could be one of the most important features of my classroom in terms of developing a growth mindset among my students. I love the blend of looking back to celebrate something and looking forward at something (and how) to improve.

I’m wondering now about the best way to incorporate this SP/STI reflection into the “aftermath” of all my assessments. The comments (see below for some samples) were physically all over the place, with some easier to read than others. It might be worth the time (and “lost” space on the page) to add a little box near the top of the assessment with room carved out for the SP and STI comments. I’ll tinker with the layout and post an update if I come up with anything promising.

Student Comments, Round 1

Here are the SP/STI reflections from the first eight papers in the stack today. Some comments are decidedly un-profound, but others are exactly what I was hoping for right out of the gate. I’m hopeful that my classroom will become a more thoughtful and reflective place through this routine. We’ll see how it goes next time.

Update from the Interwebz

@mjfenton Trying the workflow today. Will be grading today. Instead of STI and SP, I used "Praise" & "Polish" (something we used earlier)

— Jedidiah Butler (@MathButler) May 9, 2014